It does strike me that the theme of evil spoiling evil is recurring in the Lord of the Rings and does a lot to bring "the Wise" to eventual victory. I'd like to discuss, starting with a few examples

Theoden quotes this proverb in Two Towers, when Pippin has just looked into the Palantir, thereby saving Gandalf from trying it. Gandalf, of course got the palantir only because Wormtongue threw it at him, in his hatred using one of Saruman's chief treasures as a missile. Saruman is only holed up in Orthanc with Wormtongue because he's been corrupted by wanting the Ring, but he's far from a reliable ally for Sauron, and many of his actions have indirectly helped Sauron's enemies. For example, he's only under siege in Orthanc because of events that follow from his attempt to seize the Ring from the Fellowship. And that attempt went wrong partly because of squabbles between different factions in the orc raiding force. And anyway, he missed the Ring Bearer because the Ring had finally driven one of the Fellowship mad, and scared Frodo away before Saruman's orcs get to him.

Earlier in the story, Sauron is forced to send the Ringwraiths to the Shire, unsuitable as they are for a stealth mission, because any other agent who got hold of the Ring would try to keep it. The Barrow Wight's attempt to snatch the hobbits (to get the Ring? or just because they are passing?) results in them getting Nazgul-slaying weaponry, which then probably causes the Black Riders not to press their attack too hard after Weathertop.

Of course, the biggest freelancer of all is Gollum, whose attempt to get the Ring back is what allows it to be destroyed.

If evil put up a more united front, could it have been defeated at all?